3.1.9 Classification of Riemann problems

Figure 26: Different Riemann problems for Burgers' equation.

• A Riemann problem consists of a step at $x=0$ in $q$ with constant states $q_\mathrm{l}$ and $q_\mathrm{r}$ on the left and right side, see Eq. (174).
• Figure 26 shows different types of solutions with a shock (top) and a rarefaction wave (bottom).
• Except for the transonic rarefaction wave the flux across the boundary (dashed line) is either $f \! \left( q_\mathrm{l} \right)$ or $f \! \left( q_\mathrm{r} \right)$.